Unit Generators and V.I.s

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Unit Generators and V.I.s

• Patches are configurations of V.I.s
• Both Patches Virtual Instruments can be broken
  down into separate components called Unit
  Generators

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Unit Generators

• Have input parameters
• Have at least one output
• Perform a function
• modification of a signal
• combination of signals

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(No Transcript)
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Oscillators
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Oscillators

• Can be driven by an algorithm in real time
• Computers have, until recently, been too slow to
  deal with this whilst providing the user with the
  capabilities they require
• So most virtual oscillators use a waveform that
  is pre-stored in a wavetable

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Wavetables

• The value of many uniformly placed points on one
  cycle of a waveform are calculated
• These points are stored in a wavetable

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Wavetables

• A pictorial representation of a wavetable
  really its just a table of numbers

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Wavetables

• The oscillator will retrieve values from the
  wavetable to produce the wave
• The position we are at along the wave is known as
  the phase

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Phase

• The phase of the wave is its position in the
  wave cycle
• Normally measured in degrees (0? - 360?) or
  radians
• Here it is measured in sample points
• Phase (F) of 0 is the first sample

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Phase

• So if the wavetable has 512 sample points
• And the phase is 180?
• What sample point are we at?

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Phase of 180?
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Periodic Waves

• We only store one cycle of the wave because the
  wave is periodic
• This means it repeats forever

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Wrap Around

• So if we talk about a given phase F1
• F1 515
• The sample point (F) we are looking for in our
  wavetable is
• F F1 512 3

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Digital Waves Sampling Frequency

• Sound waves held digitally are cut up into small
  pieces (or samples)
• The number of samples they are cut into affects
  the smoothness of the wave
• CD sampling frequency 44,100 samps/sec

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Wave Playback

• Playing back the wave in the wavetable will
  produce a sound of a particular frequency
• Before the wave is played back it must be
  calculated and then stored
• The number of samples used to store each second
  of the waveform is known as the sampling
  frequency, fs

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Wave Playback

• When the wave is played back it is played back at
  the same sampling frequency, fs
• It is possible to figure out the frequency of the
  wave stored by performing a calculation

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Calculating the Frequency of the Wave Held in the
Wavetable

• fs / N
  f0
• samples per second / samples per cycle cycles
  per second
• (seconds/samples) / (cycles/samples)
  (seconds/cycles)

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Calculating the Frequency of the Wave Held in the
Wavetable

• fs / N f0
• 44,100/512 86.13 Hz

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Sampling Increment (S.I.)

• We dont just want 86.13Hz
• We want any frequency we want
• So we use a Sampling Increment

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Sampling Increment (S.I.)

• The sampling increment is the amount added to the
  current phase location before the next sample is
  retrieved and played back
• By altering the S.I. we can use the wavetable to
  create waves of different frequencies

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Sampling Increment (S.I.)

• Playing back the wave at 86.13Hz means playing it
  back as it is
• This means adding 1 to each phase location before
  retrieving the next sample and playing it back
• This happens 44,100 times a second, and produces
  86.13 cycles each second (because there are 512
  samples per cycle)

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Sampling Increment (S.I.)
44,100 / 512 1 86.13 Hz
fs / N S.I. f0
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Increasing Playback Frequency

• Increasing the S.I. decreases the number of
  samples played back
• So the speed of the wave playback is increased,
  as is the frequency of the wave produced

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S.I. 2
fs / N S.I. f0
44,100 / 512 2 172.27 Hz
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Rearrange the Equation
fs / N S.I. f0
S.I. N f0 / fs
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Playback Wave at 250 Hz
S.I. N f0 / fs
S.I. 512 250 / 44,100 2.902
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Table Look-Up Noise

• We only have 512 samples in our wavetable
• The points we have samples for may not line up
  with the points at which we wish to obtain
  samples
• The S.I. is 2.902 but (going from 0) we only have
  samples at 2 3

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Dealing With Real Numbers

• The samples we want to grab dont exist!
• Options
• truncate 2.902 becomes 2
• round 2.902 becomes 3
• or interpolate...

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Interpolation

• 2.902 is used as the S.I.
• so take a value at the initial phase (say 3)
• add 2.902 to the initial phase 5.902 to get the
  place to take the next value
• add 2.902 to this to get the place to take the
  next value 8.804
• and so on

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Interpolation

• we dont have values at these points so we
  calculate estimated values using the nearest
  samples (this is interpolation)

0.902 0.3 0.098 0.7 , or 90.2 of 0.3
9.8 of 0.7 0.2706 0.0686 0.3392
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Interpolation

• Occurs for every sampling increment, so 44,100
  times per second
• Uses a LOT of processing power
• The interpolation process still requires us to
  round numbers up or down, and so still produces
  error

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Table Look-Up Noise

• So rounding is required whatever, and that
  produces error
• This error is known as table look-up noise
• This error affects signal to noise ratio (S.N.R.)

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S.N.R.

• Affects the ratio achievable between quiet and
  loud sounds.
• Dodge (1997)
• Ignoring the quantisation noise contributed
  by data converters a 512 entry table would
  produce tones no worse than 43, 49, and 96 dB
  SNR for truncation, rounding and interpolation
  respectively. And a 1024 entry table would
  produce tones no worse than 109 dB SNR for an
  interpolating oscillator.

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A Sine Wave
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A Sawtooth Wave
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A Square Wave
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A Triangle Wave